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A270621
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 177", based on the 5-celled von Neumann neighborhood.
1
3, 5, 23, 1, 51, -19, 95, -83, 235, -191, 291, -191, 335, -300, 501, -441, 693, -701, 889, -745, 1001, -893, 1273, -1225, 1517, -1365, 1633, -1461, 1853, -1633, 1756, -1703, 2503, -2671, 2959, -2659, 3119, -2919, 3587, -3439, 3675, -3647, 4291, -3855, 4451
OFFSET
0,1
COMMENTS
Initialized with a single black (ON) cell at stage zero.
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
MATHEMATICA
CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=177; stages=128;
rule=IntegerDigits[code, 2, 10];
g=2*stages+1; (* Maximum size of grid *)
a=PadLeft[{{1}}, {g, g}, 0, Floor[{g, g}/2]]; (* Initial ON cell on grid *)
ca=a;
ca=Table[ca=CAStep[rule, ca], {n, 1, stages+1}];
PrependTo[ca, a];
(* Trim full grid to reflect growth by one cell at each stage *)
k=(Length[ca[[1]]]+1)/2;
ca=Table[Table[Part[ca[[n]][[j]], Range[k+1-n, k-1+n]], {j, k+1-n, k-1+n}], {n, 1, k}];
on=Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)
Table[on[[i+1]]-on[[i]], {i, 1, Length[on]-1}] (* Difference at each stage *)
CROSSREFS
Cf. A270618.
Sequence in context: A212260 A376002 A178377 * A270637 A064187 A112686
KEYWORD
sign,easy
AUTHOR
Robert Price, Mar 20 2016
STATUS
approved